A Neural Network-based Framework for Fast and Smooth Posture Reconstruction of a Soft Continuum Arm

TL;DR

The proposed fast smooth reconstruction method is shown to be five orders of magnitude faster while having comparable accuracy than past solutions to this problem are computationally intensive.

Abstract

A neural network-based framework is developed and experimentally demonstrated for the problem of estimating the shape of a soft continuum arm (SCA) from noisy measurements of the pose at a finite number of locations along the length of the arm. The neural network takes as input these measurements and produces as output a finite-dimensional approximation of the strain, which is further used to reconstruct the infinite-dimensional smooth posture. This problem is important for various soft robotic applications. It is challenging due to the flexible aspects that lead to the infinite-dimensional reconstruction problem for the continuous posture and strains. Because of this, past solutions to this problem are computationally intensive. The proposed fast smooth reconstruction method is shown to be five orders of magnitude faster while having comparable accuracy. The framework is evaluated on two testbeds: a simulated octopus muscular arm and a physical BR2 pneumatic soft manipulator.

Figures (5)

• Figure 1: (a) Cosserat rod model for a slender soft continuum arm. (b) experiment setup: a $\textnormal{BR2}$ pneumatic soft manipulator is set up in the Vicon motion capture arena. Actuation signals are generated from Raspberry-Pi 4 and relayed to SMC pressure regulators. Ring markers are designed to hold the infrared reflective tags for the Vicon system to track.
• Figure 2: Pipeline of the proposed fast smooth reconstruction method: (a) A dynamic simulator is used to generate a initial dataset $\mathcal{S}$ of soft arm deformation trajectories in a suitable workspace. (b) Principle component analysis is performed on the strain functions in dataset $\mathcal{S}$. Each type of strain is represented by a finite number of basis functions. (c) Training data $\mathcal{X}$ contains marker poses obtained from strain coefficient sampling and posture acquisition. (d) At the training stage, a multilayer perceptron neural network model is learnt in an unsupervised manner to minimize the phyiscs-informed objective function. (e) Inference stage is carried out on two testbeds: a computational octopus muscular arm and a physical $\textnormal{BR2}$ pneumatic soft manipulator.
• Figure 3: (a) Performance comparison of the proposed reconstruction method (NN) with the benchmark forward-backward algorithm (FB) in kim2022physics. Left column reports the computational time cost for one reconstruction sample. NN provides smooth posture reconstruction over five orders of magnitude faster than FB. Right column shows the normalized loss which indicates that NN achieves the reconstruction accuracy in a comparable scale to FB. The normalized loss is the loss \ref{['eq:objective']} normalized by the regularization parameter $\eta$ and the number of markers $N_\textnormal{m}$. (b) Training and validation losses over epochs for two testbeds, a computational octopus muscular arm and a physical $\textnormal{BR2}$ pneumatic soft manipulator. Each plot shows the mean and standard deviation of the training and validation losses over a total of fifty independent training experiments. Insets show the change of losses after 50 epochs.
• Figure 4: Performance of the proposed framework on the simulated octopus muscular arm model: (a) Averaged arm reconstruction error over samples for 27 targets uniformly distributed in the workspace $\mathcal{W}$. The target with maximum (minimum) averaged error is marked with black (white) circle, and on the color bar as well. (b) The target with the maximum averaged error from part (a) is chosen for plotting the arm reconstruction error $e_t$ over time. The three panels on the right demonstrate the simulated octopus arm postures at three time frames $t_1,t_2,t_3$ with their corresponding reconstructed arm postures. For each time frame, all six estimated strains $\hat{{{\varepsilon}}}_t(s)$ (in solid lines) are compared with the ground truth ${{\varepsilon}}_t(s)$ (in dashed lines) from octopus arm simulator.
• Figure 5: Performance of the proposed framework on the physical $\textnormal{BR2}$ soft manipulator: (a) Tip trajectories of the reconstructed $\textnormal{BR2}$ and the physical $\textnormal{BR2}$ (tip ring marker) from the repeated motion cycles. (b) The arm reconstruction error $e_t$ over time. The error curves are overlapped for each cycle. The three panels on the right demonstrate the camera frames of $\textnormal{BR2}$ soft manipulator, the poses from Vicon ring markers, and corresponding reconstructed smooth arm postures. Measured marker poses are rendered in grey directors to illustrate the reconstruction accuracy. For each time frame, all three estimated curvatures (angular strains) are demonstrated, and represent the pure bending, bending-twisting combination, and pure twisting.

Theorems & Definitions (1)

• Remark 1